The present invention relates to a method and apparatus for the enhancement of the rate of heat or mass transfer in a stream of liquid metal.
It is commonly accepted that the interaction between a magnetic field and a liquid metal, LM, flow leads, in a fusion reactor blanket environment, to the suppression of turbulence, and thus to a reduction in the heat-transfer rate. When the magnetic field direction is transverse to the LM flow direction, the reduction in the heat-transfer coefficient, coupled with an increase in the pressure drop along the LM coolant channel, can significantly complicate the design of self-cooled LM blankets. For example, the poloidal-flow blanket configuration (in which the lithium flows around the axis of the plasma column in, e.g., the experimental tokamak fusion reactors) was found to be geometrically the simplest among all the design options (for a self-cooled liquid metal blanket for tokamaks) considered. However, in designing this blanket it was found that the average LM velocity required to maintain the maximum interface (i.e., first-wall) temperature at an acceptable level is too high for either thermal efficiency point-of-view or from MHD pressure drop (which determines the maximum primary stress level) point-of-view. Consequently, a more complicated toroidal/poloidal geometry was selected for the self-cooled liquid metal blankets recently designed.
The analysis of the poloidal blanket (as of most, if not all, of the self-cooled LM blankets considered so far) assumed a "slug" flow regime, namely, a complete suppression of turbulence and a flat velocity profile. However, there exists experimental evidence that, in the case of a transverse magnetic field, strong residual flow disturbances persist with an increase in the field intensity even when the LM flow is "laminarized", in the sense that the friction corresponds to a laminar theory. These disturbances even strongly increase, in some cases, with an increase in the field intensity.
It is generally supposed that in the presence of a very strong magnetic field, turbulence is completely suppressed and the flow can be treated as laminar up to the highest values of Reynolds numbers typical for self-cooled, liquid metal blankets. It has been proven experimentally that this assumption is definitely valid in relation to calculation of friction (pressure drop). Indeed, the most general empirical formula for critical Reynolds number (Re.sub.cr) corresponding to laminar-turbulent transition in the presence of a transverse magnetic field is: EQU Re.sub.cr =Ha(215-85 exp (-0.35.beta.)) (1)
where .beta.=b/a is the flow channel aspect ratio of a rectangular duct having wall lengths of 2a and 2b, respectively, and Ha is the Hartman number.
Expression (1) is applicable to flows in ducts of any rectangular cross section. For a circular pipe expression (1) is also valid with .beta.=1. It turns out that for the flow conditions typical for fusion reactor blankets, Re&lt;Re.sub.cr so that the pressure drop can be calculated assuming that the flow is laminar.
The situation is not as clear in the case when liquid metal flows parallel to the magnetic field, particularly when the flows are initially turbulent. Friction decreases under a strong parallel magnetic field, but "pure" laminar friction has not yet been observed.
Experimental studies which were carried out in accordance with the present invention indicate that even in the case of transverse flow, the turbulence suppression phenomena are much more complicated than just a gradual decrease of turbulent velocity fluctuations and their eventual disappearance with the increase in the field intensity. As observed, even after the flow is "laminarized" in the sense that the friction corresponds to laminar theory, strong residual flow disturbances still exist. These disturbances can strongly increase in some cases when the magnetic field increases. Thus it has been established that the presence of a strong transverse magnetic field, which suppresses the velocity fluctuation parallel to the field, can, as a result of an inverse energy cascade, both enhance the velocity fluctuations perpendicular to the field and increase the integral scale of turbulence. The resulting strongly non-isotropic turbulent field causes no substantial momentum transfer (i.e., no pressure drop enhancement), but can enhance heat transfer.